The Monkeys are Typing Again . . .

Recently I was read a series of email exchanges between a good member of the church and a Utah political leader. The writer was mistakenly concerned that religion and evolution were at odds and argued that intelligent design should be taught as science. This person promoted a common argument against evolution seen in creationist attacks, but it shows a basic misunderstanding about evolution and presents a straw argument against evolution. They suggest evolutionists believe that random processes alone structure the universe and evolution is an argument about low probably events occurring. This argument assumes that evolutionists think that if an infinite number of monkeys, given infinite time, are put to typing on typewriters that eventually the complete works of Shakespeare will inevitably result. Of course, the Intelligent Design creationists then point out that it is so improbable as to be impossible, therefore evolution is false. I say give the monkeys a chance. Let’s set some monkeys to typing and see if evolution is true or not. Science is about experimentation and nobody has even done any monkey on typewriters work.

The trouble with this argument is that this misrepresents evolution so completely as to be almost a ludicrous caricature. It suggests that because evolution works on random processes that the appearance of life on earth is a random probabilistic event.

Do evolutionary thinkers honestly believe that DNA just appeared on earth just by random chance? No they do not. The power of evolution is that it is a mechanism that creates complexity from simplicity (creationist sometimes argue that the second law of thermodynamics prohibits simplicity from moving to complexity, however, remember that is true only of closed systems, the sun is pouring enormous energy into the Earth which allows the move from simplicity to complexity). Evolution does not start with a random string of DNA suddenly and probabilistically appearing ex nihilo. It starts with a simple system that can replicate itself. All it takes is one chemical that can copy itself—one molecule that produces a molecule just like itself, some random variation and a selective environment. Once that is in place then evolution can work its wonders.

This view of evolution as random events only does not engage the views of real biologists. The missing piece of this argument is that evolution occurs through selection on random processes, not that life is just a random event. The whole genius of Darwin was natural selection. Selection! Not just random processes willy-nilly creating life.

Evolution through natural selection is a sorting algorithm. Let’s take our Monkeys busily typing away at their typewriters (I actually saw a creationist attack on this by giving monkeys typewriters and watching them destroy the ill-fated machines–somehow this was supposed to show the absurdity of evolution. I think the reasoning the authors were going for was something along the lines of (A) Since monkeys could never type at all, then (B) they could never produce Shakespeare, hence evolution is false since it relies on something Huxley is supposed to have said about monkeys typing.) Now, just as a point of clarification, Huxley never said this to Bishop Wilberforce in their famous debate, but let’s go with the analogy anyway. Evolution does not just argue that the complexity of life just jumped from nowhere in some probabilistic leap from the void, rather it argues that selection acts on random variation. Moreover, once something arises through random mutation that is adaptive it keeps it. So instead, as this author argues, of our waiting around for the monkeys to type the sonnet by randomly pecking at the keys, which we agree is not very likely, we get to keep those that fit the pattern provided by the sonnet. So suppose that every time a monkey hits a letter that belongs in the appropriate place in the sonnet our sorting algorithm keeps it. So for example, if our monkey hits an ‘a’ in the place where there is supposed to be an ‘a’ in the sonnet then it remains. I show below that it only takes about 240,000 key strokes under selection to get our sonnet. Far less than the 1/30527 you obtain get in the creationist attack as the probability of getting the sonnet. Interestingly, the probability of the monkey’s getting the sonnet? Probability = 1. It’s inevitable under Darwinian selection. (For a more complete assessment of how long it would take to get the 1000 lines of Shakespeare see the end of this Blog) We could even add a mutation rate and still get our monkey-typed sonnet in a reasonable time. (In fact, in Richard Dawkins Book The Blind Watchmaker he programs this process on his computer and gets lines from Shakespeare very rapidly using random variation with selection.) The point is that if you add selection to a process, very improbable events can jump to inevitable. And evolution is all about selection. In biological evolution, it is the environment that decides what is kept rather than someone watching the keys, but the principal is the same. So when selection acts in combination with random variation (our monkeys typing) the wondrous adaptations we see in the natural world are not infinitely unlikely. No. Using the power of evolution, these things can be explained quite easily. In fact evolution is currently being used to solve intractable mathematical problems that were thought to be unsolvable. In fact, software engineers use evolution to solve real-world problems; complex programs are evolved to solve engineering and mathematical problems by using random variation, inheritance, and selection—the only necessary ingredients for evolution.

Appendix A (you don’t have to read this: it’s math).

How long would it take the Monkeys to type out a Shakespearean sonnet under Darwinian Selection?
Consider an N character sonnet (or any given string of N characters). Now for each of those characters, the probability that the monkey’s key stroke will match the required letter in the i_th place is 1/(number of letters) for each position. Call this s. I’m assuming here that each of the monkey’s keystrokes is independent, uniformly distributed. For simplicity sake let’s assume that the monkeys complete a discrete round of N characters every T seconds call these rounds 1, 2, . . ., j, . . .t. (if you assume continuous typing it can only reduce the time it take to reach the sonnet i.e. this is a conservative assumption). Now assume every time the monkey’s stroke matches the character in position i, that that character is fixed, i.e., selection acts to keep that character because it matches the character in that string (like gene that produces a trait that fits in the current environment). Therefore, in the first round (1- s)*N characters remain unfixed and remain the same in all the rounds thereafter. In the second round there will be (1- s)*N*(1- s) or (1- s)^2*N unfixed. Using induction it can be shown (yes mathematicians talk this way! Not ‘I show’, but it can be shown!) that in the tth round there will be (1- s)^t*N characters that remain to be fixed. The time until fixation of the entire sonnet then is when s^t*N < 1, there are less than 1 characters needing to be fixed and no characters remaining to be fixed. At that time the monkey’s typing matches the desired string. Algebraically, this can be shown to be when t > ln(1/N)/ln(1- s). Let’s consider a sonnet of 1000 characters and with about 30 characters in the alphabet (I’m including some punctuation): then s = 1/30, N = 1000 and so our Monkeys will reach their goal in about 204 rounds or about 240,000 key strokes if they uselessly pound on fixed position keys or 28,972 if they quit hitting keys that have become fixed. As you can see it is no problem to get a sonnet for ambitious monkeys, a sorting algorithm, and some random variation. Monkeys prove evolution again! Doesn’t it make you proud that our physical bodies came from such distinguished and versatile characters!

11 Responses to The Monkeys are Typing Again . . .

Thanks for your clarity on evolutionary thinking. It is nice to run into a fellow LDS evolutionist. You might be interested in some of my essays at “Mormon Insights,” especially my essay Evolutionary Science Inspires Me.

I also think that evolution was the mechanism by which God created the diversity of life on the earth, but I have some issues with your comments here.

First, I’ve never understood why some evolutionists are so adamant in saying that natural selection isn’t chance. Whether it’s one big chance leap to the precipice of Richard Dawkin’s “Mount Improbable” or a bazillion little chance steps up the hillside, we’re still talking random chance, are we not?

Second, the way you (and Dawkins) have set up the monkeys and typewriters by matching the keystrokes with a predetermined sonnet strikes me as loading the dice. Likewise with the engineering algorithms you mentioned; the complexity is pre-programmed into the algorithm in the form of constraints that guide it towards the desired outcome. A more compelling example would be if you showed a random string evolve into a whole new sonnet. Theoretically it’s plausible, but this would obviously require more than 240K keystrokes, so is it probable?

And I guess that’s the main question of Intelligent Design advocates. Not whether it could happen, but given the complexity of the human genome would it happen in a conceivable amount of time, say, before the heat death of the universe?

I will throw this out to anyone here. I have no problem with evolution, as long as it includes an Adam and Eve in it. I am not so concerned with when they lived, as long as they did live.

Awhile back there was a discussion on LDS-Phil about this, and it became the general consensus, that there must be an Adam and Eve. Otherwise, it would not fit within the context of Christianity, and therefore Mormonism.

First, great stab at a tricky subject. I am eagerly anticipating the future posts on this great new blog.

Second, let me say that I am on the bloggers side, a committed member of the LDS church and a research scientist who embraces evolution. The problem I have is that the person defending intelligent design above is absolutely right about loaded dice. The complexity is preprogrammed into the monkey example above. A “goal” was stated, and achieved by an ad hoc process of selection. This is only a reasonable assumption for the simplest evolutionary scenarios, such as bacteria in a petri dish subjected to antibiotics and evolving antibiotic resistance. It also is at odds with how most evolutionary biologists think of evolution, that selection is not guiding life toward any concrete goal, but rather simply reflects the tendency of some mutations to do better than others, with a compounding effect over time leading in no particular (imposed) direction.

For longer term processes, selection needs to be conceptualized as emerging from the interactions between the different organisms, the scales of the resources being used, etc. depending on the context. This is a much more interesting and difficult problem, and the answer as to how complexity emerges is no longer obvious at all. In the language of physics, this problem is “strongly correlated.”

This does not mean that evolution is wrong. On the contrary, it is simply much more interesting and exciting than the monkey example would indicate. We even know a little bit about how to think about these problems. There are all kinds of examples in nature where even inanimate objects such as molecules, spontaneously assemble themselves in the most striking and complex ways without a preordained design. Give a bunch of monkeys a bunch of tinkertoy water molecules and see if they ever come up with the crystal structure of ice, let alone a snowflake! I imagine it is as hard as a sonnet, at least. Yet the molecules do it spontaneously, every time the temperature goes below a certain point, with no guiding hand, in ways that are well understood to the point of having predictive, quantitative models of freezing and snowflake formation based solely on the physics of the molecules. Astonishing, if you think about it (even more astonishing if you realize that giving the tinkertoys to undergraduate chem majors instead of monkeys may not speed it up much beyond the monkeys).

I think that evolution is much more like ice freezing than the monkey example above, a collective effect. Given the enormous variety of materials to nature has to work with, and our experience with spontaneous order and complexity in simple systems, the spectacular dynamical order and complexity of life and evolution seems beautiful, but not that improbable. Scientists who study evolution from the perspective of emergent order and complexity are already producing some beautiful examples of how complexity in life can emerge generically without loading the dice (See, e.g. Guttenberg and Goldenfeld’s beautiful, if abstract work at http://arxiv.org/abs/0707.4533) . And thus we see the beginning of the closing of the gap in which the “god of the gaps” ideas of ID reside.

I do find the idea of emergent complexity interesting. Fractals, iterated function systems, nonlinear dynamics, attractors, bifurcations, phase-locking etc. do seem to be a much more promising vocabulary for evolution than the current existing Darwinian mechanisms.

However, I think that there are fundamental differences between the kind of self-organizing complexity one sees in a snowflake, or a Mandelbrot set, and that of living things. While a snowflake is complex, its information content is low. I think that there is danger in confusing the medium with the message. The information contained in DNA is distinct from the medium (the actually molecule) that stores and coveys that information just as the meaning of this post is distinct from the bits, bytes, pixels, and letters it is stored in. Evolution needs to account for how the information arose in the first place. Evolution claims that the semantics that make life arose from the syntax.

Since I am a proponent of Front-loaded evolution, I would be interested in seeing how that concept could be married to that of the science of complexity and emergent systems.

If you were truly concerned about those who speak as if “science and religion were at odds”, it seems that you would save some of your energy for the scientists who make that suggestion rather than expending it all the religionists. When can we expect your takedown of Richard Dawkins to appear?

I to am a member of the Church of Jesus Christ of Latter Day Saints BUT I DON’T Support evelution and i am very disappointed that any LDS would even think of embracing it. i hope you weren’t being serious when you said “Doesn’t it make you proud that our physical bodies came from such distinguished characters?” or something like that. Well no even if i did believe in evolution i would not be proud of coming from a monkey. I KNOW WHERE I COME FROM, and i was created in God’s image alone, and monkeys were created in the image of monkeys, and fish came from fish. YOU CAN’T GET HUMANS FROM MONKEYS!!! YOu say that you are a member of the church of Jesus Christ of Latter Day Saints, but you are not stading up for what you have learned in church all these years, you’ve let something get in the way. Please when you read this turn to you Bible and read Genesis chapter 1, this is the way it happened and that is all that we should teach in our schools. Please remember who we are. we are saints of the true and living God, not searvant to evolution. You all might be from Utah and have a heap of Lds saints everywhere, but i live in Arkansas and and my faith is tried often by my loneliness, but it has taught me to be true to the gospel. please do not love evolution more than the gospel, because it will become your god and things won’t work out for the best for you, KEEP THE COVENANT!!!